Spreading Resistance in Flux Tubes With Variable Heat Flux and Nonuniform Convection

Abstract

cylindrical-shaped flux tubes with variable heat flux distributions and nonuniform heat transfer coefficients are obtained. The solutions are presented based on the method of separation of variables combined with the method of least squares in the cylindrical coordinate system. In the source region, a variable heat flux modeling function is considered. The modeling function depends on a distribution parameter, where different distributions can be defined by changing the value of this parameter. Along the sink region, a nonuniform heat transfer coefficient with a distribution parameter is considered. The sink distribution parameter can define a wide variety of different conductance distributions, from intense conductance under the source area to a uniform conductance along the entire sink plane. The developed solutions are used to evaluate the nondimensional total thermal resistance for different nondimensional parameters, represented by the heat-source aspect ratio, thickness aspect ratio, Biot numbers, flux distribution parameter, and conductance distribution parameter. The solutions are used to examine the effects of different conductance distributions on the nondimensional total thermal resistance for three different heat flux distributions. Furthermore, numerical results based on the finite-element method are obtained for some of the conducted studies to verify the analytical results, where very good agreement has been observed.